In his comments to the court, he said he "agreed with other persons in or around 1992 to facilitate the acceptance of a bribe in conjunction with the selection of the host nation for the 1998 World Cup". France beat Morocco in the contest to hold that tournament.
Mr Blazer added that between 2004 and 2011, he "and others on the Fifa executive committee agreed to accept bribes" in connection with South Africa's winning bid to host the 2010 World Cup championship.
Asked if he was pleading guilty of his own free will, Mr Blazer replied: "Totally."
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Mr Blazer is a key figure in the US government's corruption case against nine Fifa officials and numerous sports marketing executives. His guilty plea in 2013 took place in secret and his role as a US informant only became public last week.
Mr Blazer also admitted to taking bribes in connection with multiple sports marketing contracts for Concacaf Gold Cup tournaments between 1996 and 2003.
The transcript reveals few new details about Mr Blazer's role in the scheme or other schemes. Authorities have said their investigation is in the early stages but people familiar with the matter have said that the FBI is investigating whether bribes were paid to affect the awarding of the World Cup tournament to Qatar and Russia for 2018 and 2022.
Mr Blazer arrived at court in a wheelchair, according to the transcript, and told the judge he was suffering from rectal cancer, but his prognosis was "good".
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"Beginning in or around 2004 and continuing through 2011, I and others on the Fifa executive committee agreed to accept bribes in conjunction with the selection of South Africa as the host nation for the 2010 World Cup. Among other things, my actions described above had common participants and results," Mr Blazer told Judge Raymond Dearie.
Mr Blazer also admitted to defrauding the Internal Revenue Service of taxes, including by failing to disclose bank accounts in the Bahamas.
The portion of the transcript that was redacted followed a question by the judge as to whether there was "anything else", and also appeared to relate to conditions of Mr Blazer's bail, which the judge set at $10m.
Prosecutors argued to keep those portions of the transcript hidden, which the judge granted.